Optical spectra of biological polymers contain important information about their structure and function in living organisms. This information can be accessed by extracting an optical interaction of monomers, i.e., their exciton coupling, from experimental data. This coupling is sensitive to molecular structure, geometry, and conformation and can be used to characterize them. However, the accurate determination of exciton coupling in important biological molecules is difficult because inhomogeneous broadening smears out the monomer interaction. We suggest a way to overcome this problem by applying exact sum rules. These sum rules are derived by establishing a straightforward relationship between integral characteristics of absorption and circular dicroism spectra, and exciton coupling. Exciton coupling between AT pairs in native DNA conformation is estimated by applying these sum rules to DNA hairpin optical spectra as V(0) approximately 0.035 eV in agreement with the earlier numerical calculations.